Question

The sum of the interior angles of a triangle is 180˚, The second angleof a triangle is 45˚ more than the first and the third angle is twice thefirst.

Answer 1

Step-by-step explanation:

The sum of interior angles of a triangle is

`180^0`

Let the first angle be represented as

`x`

The second angle of a triangle is 45˚ more than the first

This will be represented below as

`x+45`

The third angle is twice the first.

This will be represented below as

`2x`

To figure out the value of the angles, we were given that the sum of angles in the tirangle is 180

Hence,

We will have the expression represented below as

`\begin{gathered} x+(x+45)+2x=180^0 \\ firstangle+secondangle+thirdangle=180^0 \end{gathered}`

By collecting similar terms, we will have

`\begin{gathered} x+(x+45)+2x=180^0 \\ x+x+2x+45=180^0 \\ 4x+45=180^0 \\ substract\text{ 45 from both sides, we will have} \\ 4x+45-45=180-45 \\ 4x=135^0 \\ divide\text{ both sides by 4} \\ (4x)/(4)=(135)/(4) \\ x=33.75^0 \\ secondangle=x+45=33.75+45=78.75 \\ thirdangle=2x=2*33.75=67.5^0 \end{gathered}`

Hence,

The final answers are

`\begin{gathered} first\text{ }angle=33.75^0 \\ second\text{ }angle=78.75^0 \\ third\text{ }angle=67.5^0 \end{gathered}`